I suggest using PodBean. You have to register, but it's free. You can upload .mp3 files to it, and make music players with them. Plus, if you add width="0" height="0" to the code of the player and make sure it autoplays, what you want is definately possible.

Sorry I took so long to reply. Simply change the red part of the link below to your Podbean Account Username. There will be a big upload button on the page http://PODBEANUSERNAMEHERE.podbean.com/admin/filemanager-index.php